Wienerization Based Control of Nonlinear Systems

Abstract

We present a novel model approximation scheme, named “wienerization”, of nonlinear time invariant systems that uses the systems' nonlinear equilibria maps as the static nonlinearities of Wiener models. We show conditions for when controllers based on such wienerization schemes exploiting correct system equilibria maps lead to asymptotically vanishing tracking errors. Furthermore, we show that this modeling scheme can be used to improve closed loop control of nonlinear systems without the need for modifying a preexisting linear controller nor re-tuning it, but rather simply adding opportune nonlinear static maps to the reference and output signals. To this end, we demonstrate a novel controller retrofitting scheme that may be implemented following an arbitrarily smooth transition from the original controller to the modified, improved one.